seismic assessment of masonry ‘‘gaioleiro’’...

Journal of Earthquake Engineering, 14:80–101, 2010

Copyright � A.S. Elnashai & N.N. Ambraseys

ISSN: 1363-2469 print / 1559-808X online

DOI: 10.1080/13632460902977474

Seismic Assessment of Masonry ‘‘Gaioleiro’’Buildings in Lisbon, Portugal

NUNO MENDES and PAULO B. LOURENCO

Department of Civil Engineering, ISISE, University of Minho, Guimaraes,

Portugal

This article presents a numerical study for the seismic assessment of a Portuguese building masonrytypology - ‘‘Gaioleiro.’’ Numerical analysis was performed using a finite element model calibratedwith experimental results obtained in 1:3 reduced scale tests carried out in the LNEC 3D shakingtable. Nonlinear dynamic analysis with time integration and pushover analysis are carried out.

Using nonlinear dynamic analysis it was verified that the buildings of ‘‘Gaioleiro’’ type withappropriate floor-wall connections are in the limit of their loading capacity. The pushover analysesperformed in this study were incapable of simulating correctly the damage of the structure underseismic action.

Keywords ‘‘Gaioleiro’’; Buildings; Masonry; Earthquake; Seismic Assessment; Nonlinear TimeHistory Analysis; Pushover Analysis

1. Introduction

Earthquakes are known by their catastrophic effects. Information from the United Nations

reveals that the percentage of deaths originated by phenomena of seismologic character

was 26% of the total number of casualties caused by natural disasters, with an estimate of

more than fourteen million of victims since 1755 [Barbat et al., 2006].

It is not possible to act on the seismic hazard, meaning that mitigation of the seismic

risk can only be made through reduction of the vulnerability. The study of seismic

vulnerability can address new and existing buildings. Enough scientific knowledge

seems to be available to design structures with appropriate seismic safety. The difficulty

can be to guarantee that the regulations are fulfilled and that the execution follows

correctly the structure design [Oliveira, 2004].

The study of ancient buildings has been, in general, limited. Only in the past decades

has this issue been taken into account due to the increasing interest in the conservation of

the built heritage and the awareness that life and property must be preserved. With respect

to the built heritage, masonry buildings represent a major part of the stock and they were

often non engineered or not designed with reference to any particular code [Benedetti

et al., 1998].

In Portugal, the Portuguese Society of Earthquake Engineering (SPES) and

the Portuguese Association of Companies for Conservation and Restoration of the

Architectural Heritage (GECoRPA) elaborated a reduction program of the seismic

vulnerability of the building stock [SPES and GEOeRPA, 2001]. The objective is to

evaluate and reduce the seismic vulnerability through seismic retrofitting of the building

Received 16 July 2008; accepted 10 April 2009.

Address correspondence to Nuno Mendes, Department of Civil Engineering, University of Minho,

Guimaraes Portugal; E-mail: [email protected]

80

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stock, similarly to programs executed or proposed in others seismic countries (USA, New

Zealand, Japan, Italy, and Turkey). This program was prepared taking into consideration

the most recent methods of large scale seismic assessment. For this purpose, a represen-

tative building of a certain typology should be selected and, through the analysis of the

individual representative building, the seismic performance of the typology is estimated.

The present study is focused on this sought reduction of the seismic vulnerability of

the building stock, aiming at evaluating the seismic performance of the ‘‘gaioleiro’’

buildings (Fig. 1). This building typology developed between the mid 19th century and

beginning of the 20th century, mainly in the city of Lisbon, still remains much in use

nowadays. These buildings characterize a transition period from the anti-seismic practices

used in the ‘‘pombalino’’ buildings originated after the earthquake of 1755 (see, e.g.,

Ramos and Lourenco, 2004), and the modern reinforced concrete frame buildings. The

‘‘gaioleiro’’ buildings are, usually, four or five stories high, with masonry walls and

timber floors and roof. The external walls are, usually, in rubble masonry with lime

mortar [Pinho, 2000]. In the urban areas these buildings are usually semi-detached and

belong to a block of buildings. Although it is not an objective of this article, pounding can

be taken in account when the adjacent buildings present different heights or the separation

distance is not large enough to accommodate the displacements [Gulkan et al., 2002;

Viviane, 2007]. It is noted the ‘‘block’’ effect is usually beneficial and provides higher

strength of the building, as shown in Ramos and Lourenco [2004].

In the seismic assessment of the ‘‘gaioleiro’’ buildings, nonlinear dynamic and static

analyses were performed. The numerical model was calibrated with experimental results

obtained in 1:3 reduced scale tests including only the dead load. Subsequently, after

calibration, the model was changed and the live load prescribed in the code was added.

Furthermore, in the experimental tests the seismic action was defined according

the Portuguese Code [RSA, 1984] and in the numerical analyses the Eurocode 8

[EN 1998-1, 2004] and the Portuguese National Annex were used. This procedure is

justified as the aim of the work is to evaluate the seismic performance of the ‘‘gaioleiro’’

buildings under the present safety requirements.

2. Experimental Program

The National Laboratory of Civil Engineering, Lisbon (LNEC), carried out a set of

shaking table tests with the purpose of evaluating the seismic performance of the

‘‘gaioleiro’’ buildings, before and after strengthening [Candeias et al., 2004]. In the test

FIGURE 1 Examples of ‘‘gaioleiro’’ buildings, Lisbon, Portugal.

Seismic Assessment of Masonry ‘‘Gaioleiro’’ Buildings 81


program, a prototype of an isolated building was defined, constituted by four stories with

an interstory height of 3.60 m, 2 opposite facades with a percentage of openings equal to

28.6% of the facade area, 2 opposite gable walls (with no openings), timber floors, and a

gable roof.

Due to the size and payload of the shaking table, the experimental model was built

using a 1:3 reduced scale, taking in account Cauchy’s law of similitude (Table 1). The

geometric properties of the experimental model result directly from the application of the

scale factor to the prototype, resulting in a model with 3.15 m wide, 4.8 m deep, and 0.15

m of wall thickness (Fig. 2). The experimental model only has the top ceiling, due to

difficulties in reproducing the gable roof at reduced scale.

TABLE 1 Scale factors of the cauchy similitude [Carvalho, 1998]

(where p and m designate prototype and experimental model,

respectively)

Parameter Symbol Scale factor

Length L Lp/Lm=l=3Young’s Modulus E Ep/Em=l=1Specific mass r rp/rm=l=1Area A Ap/Am=l

2=9

Volume V Vp/Vm=l3=27

Mass m mp/mm=l3=27

Displacement d dp/dm=l=3Velocity v vp/vm=l=1Acceleration a ap/am=l

-1=1/3

Weight W Wp/Wm=l3=27

Force F Fp/Fm=l2=9

Moment M Mp/Mm=l3=27

Stress s sp/sm=l=1Strain e ep/em=l=1Time t tp/tm=l=3Frequency f fp/fm=l

-1=1/3

0.40.375 0.3

0.3

0.9

3.15

0.3

0.9

0.3

0.9

0.3

0.9

4.15

4.80

4.15

0.15

AA

'

3.15

(a) (b) (c)

FIGURE 2 Experimental model (dimensions in meters): (a) facade; (b) side (gable)

wall; (c) plan.

82 N. Mendes and P. B. Lourenco


The external walls, originally built in poor quality rubble masonry with lime mortar,

were replaced by a self compacting bentonite-lime concrete, studied to reproduce the

mechanical characteristics of the original masonry walls, namely with respect to com-

pressive strength, tensile strength, and Young’s modulus.

In the construction of the timber floors, medium-density fiberboard (MDF) panels

connected to a set of timber joists oriented in the direction of the shortest span were used.

The panels were cut in rectangles of 0.57 m · 0.105 m and stapled to the joists, keeping a

joint of about 1 mm for separating the panels. The purpose was to simulate flexible floors

with very limited diaphragmatic action (Fig. 3).

As mentioned above, a model without strengthening and models with different

techniques of strengthening were tested [Candeias et al., 2004]. In the present study,

reference is made to Model 0 (without strengthening and weak wall-to-floor connection)

and Model 1 (strong wall-to-floor connection). In the wall-to-floor connection, steel

connectors and fiber strips glued with epoxy resins were used. The strong connection

was made only in the 3rd and 4th floors near the piers (facades) and on the supports of the

joists (gable walls). Figures 4a and 4b show Model 0 and the details of the connections

used in Model 1, respectively.

The dynamic tests were performed on the LNEC triaxial shaking table by imposing

time series of artificial accelerograms compatible with the design response spectrum

defined by the present Portuguese code [RSA, 1984] for zone A and very stiff soil. The

time series were imposed with increasing amplitude and in two uncorrelated orthogonal

directions. Before the beginning of the tests and after each time series, the dynamic

properties of the models were characterized [Candeias et al., 2004]. The time series in the

two orthogonal directions are uncorrelated and should present the same PGA. However,

due to experimental difficulties in the tests, the PGA in the longitudinal direction is about

1.4 times of PGA in the transversal direction.

Figures 5a and 5b present the damage details of the Model 0 and Model 1 after

testing, respectively.

3. Definition and Calibration of the Numerical Model

3.1. Definition of the Numerical Model

The numerical model of the building was prepared using the Finite Element (FE) software

DIANA [2005], by using shell elements for the simulation of the walls and three-

dimensional beam elements for the timber joists, all based on the theory of Mindlin-

Reissner. In the modeling of the floors, shell elements were also used with the purpose of

Pine wood joists 0.10x0.07

Pine wood joists 0.03x0.15

MDF panels 0.012stapled to the joists

Pine wood rim joist0.03x0.075

Connection bars0.02

0.07

5

0.03 0.27 0.250.1

0.15

FIGURE 3 Floors (Sec. AA’ from Fig. 2).



simulating the in plane deformability (Fig. 6). In the supports, only the translation degrees

of freedom in the base were restrained. The full model involves 5816 elements (1080

beam elements and 4736 shell elements) with 15,176 nodes, resulting in 75,880 degrees

of freedom (DOF).

The behavior of the connection between the floors and the walls is unknown, as no

measurements were taken for a possible separation and the eigenmodes in the long-

itudinal direction were difficult to characterize due to presence of noise. Thus,

FIGURE 5 Cracks patterns: (a) Model 0; (b) Model 1.

FIGURE 4 Experimental models: (a) Model 0; (b) details of the Model 1 wall-to-floor

connection.



preliminary numerical analyses were made with the purpose of validating the assumption

used for the facade-wall connection.

Preliminary numerical analyses were carried out using the artificial accelerograms

used in the tests, with the lowest peak ground acceleration. It is noted that the behavior

of the Models 0 and 1 are similar for low acceleration amplitudes (PGAlongitudinal =

0.9 m/s2), and the response is basically linear elastic. The following extreme hypoth-

eses for the connection of the facades to the floors were adopted: (a) the translation

degrees of freedom are fully tied; (b) there is no horizontal connection between walls

and timber floors.

After an iterative process for proper selection of the material properties, it

was concluded that the hypothesis of a model with full translational wall-floor connection

is the most appropriate. Figure 7 shows the behavior at the top of the structure without

and with connection of the floors to the walls. It is noted that in the hypothesis of

model without wall-floor connection the facades vibrate almost independently from the

remaining structure. This behavior does not hold in the hypothesis of the model with

wall-floor connection, which is in correspondence with the observed experimental model

behavior.

As full wall-floor connection better approaches the linear behavior of the structure,

this model was adopted for calibration of the dynamic characteristics of the structure:

frequencies and modes of vibration.

3.2. Calibration of the Numerical Model

Calibration of the numerical model was accomplished with the methodology proposed by

Douglas-Reid [1982], in which the frequency i of the structure f Di can be estimated by

means of:

f Di ðX1;X2; :::;XNÞ ¼ Ci þXN

k¼1

AikXk þ BikX2k

� �; (1)

where Xk(k=1,2,. . .,N) are the variables to calibrate and Aik, Bik, and Ci are

constants.

FIGURE 6 Numerical model: (a) global view of the finite element mesh; (b) floor

elements.



The (2N+1) constants can be obtained by the following system of equations:

f Di ðXB1 ;X

B2 ; :::;X

BNÞ ¼ f Ci ðXB

1 ;XB2 ; :::;X

BNÞ

f Di ðXL1 ;X

B2 ; :::;X

BNÞ ¼ f Ci ðXL

1 ;XB2 ; :::;X

BNÞ

f Di ðXU1 ;X

B2 ; :::;X

BNÞ ¼ f Ci ðXU

1 ;XB2 ; :::;X

BNÞ (2)

. . .

f Di ðXB1 ;X

B2 ; :::;X

LNÞ ¼ f Ci ðXB

1 ;XB2 ; :::;X

LNÞ

f Di ðXB1 ;X

B2 ; :::;X

UN Þ ¼ f Ci ðXB

1 ;XB2 ; :::;X

UN Þ;

where f Ci are the frequencies calculated by means of the numerical model,

XBk (k=1,2,. . .,N) are the base values of the variables, and XU

k (k=1,2,. . .,N) and

XLk (k=1,2,. . .,N) are their respective upper limit and lower limit values.

–6

–4

–2

0

2

4

6

0 1 2 3 4 5 6Time [s]

Acc

eler

atio

n [m

/s2 ]

Acc

eler

atio

n [m

/s2 ]

P15 experimentalP15 numerical

15

(a)

0 1 2 3 4 5 6Time [s]

(b)

–6

–4

–2

0

2

4

6P15 experimentalP15 numerical

15

FIGURE 7 Acceleration at facade top: (a) with wall-to-floor connection (all translation

degrees of freedom tied); (b) without wall-to-floor connection (vertical translation

degrees of freedom tied).



After calculating the constants, an optimization process of the calibration variables is

used, with the purpose of minimizing the following equation:

J ¼Xm

i¼1

wi "2i (3)

with

"i ¼ f EMAi � f Di ðX1;X2; :::;XNÞ (4)

where f EMAi are the experimental values of the frequencies and wi are the weight factored.

In the present study, the numerical model was calibrated using the first two natural

frequencies obtained in the modal identification (first translational mode and first

torsional mode), defining as variables to calibrate the Young’s modulus of the different

materials. After an optimization process carried out using the software GAMS [1998], the

optimal values of the Young’s modulus were obtained (Table 2). It is noted that the low

value found for the Young’s modulus of the MDF panels is due to the floors arrangement

(open joints). Table 3 presents the values of the frequencies after calibration.

It is known that this building typology presents physical nonlinear behavior under

acceleration time series with larger values of PGA (PGA > 0.9 m/s2). Thus, the behavior

of the structure under the highest acceleration series of the tests (PGA = 9.75 m/s2) was

studied with the purpose of obtaining a crack pattern similar to the one obtained in the

tests. In these analyses only the physical nonlinear behavior of the masonry walls was

considered.

For this purpose, reasonable nonlinear properties were initially assumed for the

masonry material with adjustments in the fracture energies so that the crack pattern

presented in Fig. 8 could be found. It is verified that the numerical model is able to

simulate correctly the behavior of the experimental model with appropriate wall-floor

connection (Model 1), in which damage concentration at the 4th floor is highlighted.

The physical nonlinear behavior of the masonry walls was simulated using the Total

StrainCrackModel detailed in [DIANA, 2005]. This includes a parabolic stress-strain relation

for compression, where the compressive strength, fc, is equal to 0.8 N/mm2 and the respec-

tively fracture energy,Gc, is equal to 1.25N/mm. In tension, an exponential tension-softening

TABLE 2 Linear elastic properties

Young’s modulus

[N/mm2] Poisson’s ratio

Specific mass

[Kg/m3]

Walls 779 0.2 1910

MDF panels 240 0.3 760

Wood joist 12000 0.3 580

TABLE 3 Numerical frequencies after calibration

1st Transversal mode 1st Distortion mode

Numerical [Hz] 4.80 9.23

Experimental [Hz] 4.73 9.09

Error [%] 1.48 1.54



diagram was adopted, where the tensile strength, ft, is equal to 0.125 N/mm2 and the

fracture energy, Gt, is equal to 0.125 N/mm. The crack bandwidth, h, was determined as a

function of the finite element area, A (Eq. (5)). In terms of shear behavior, a constant shear

retention factor equal to 0.01 was adopted. Figure 9 presents the hysteretic behavior adopted

for the masonry.

h ¼ffiffiffiA

p(5)

Damping, C, was simulated according to Rayleigh viscous damping [Chopra, 2000],

which is a linear combination of the mass, M, and of stiffness, K, matrices (Eq. (6)).

Constants a (2.18) and b (0.00044) were determinated from the results obtained in the

dynamic identification tests (Table 4). In the damping identification, a curve fiting of the

Frequency Response Function (FRF) for a Single Degree of Fredom was used.

C ¼ �M þ �K (6)

FIGURE 8 Damage after testing in the model: (a) numerical; (b) experimental

(Model 1). (e1 is the principal tensile strain, which is an indicator of crack width).

Loading Reloading

fc

fc

εε

ε

σ

Loading

Reloading

Unloading Unloading

i

3di+

di

i

FIGURE 9 Adopted hysteretic behavior of masonry.



3.3. Incorporation of Live Load

The experimental model only considered the self-weight of the walls and of the floors. In

the calibrated numerical model, all code loads are now considered, including the self

weight of the partition walls, cladding and roof, and the quasi-permanent part of the live

load. Figure 10 presents four mode shapes in the transversal and longitudinal directions of

the calibrated model with additional mass.

Using the calibrated model with the code masses, a safety analysis is now made using

nonlinear time history analysis (Sec. 4) and pushover analysis (Sec. 5).

4. Nonlinear Time History Analyses

4.1. Seismic Action

The horizontal seismic action is described by two orthogonal and independent compo-

nents, represented by the same response spectrum. Three earthquakes were used, com-

posed of two uncorrelated artificial accelerograms (Earthquake 1, 2, and 3). The artificial

accelerograms are compatible with the elastic response spectrum (Type 1) defined by

Eurocode 8 [EN 1998-1, 2004], for the zone of Lisbon, with a damping ratio x equal to

5% and a type A soil (rock). The accelerograms were generated using the software

SIMQKE_GR [Gelfi, 2006], with a baseline correction using SeismoSignal

[Seismosoft, 2004]. Due to the fact that nonlinear dynamic analyses are very time

TABLE 4 Experimental modal damping ratio

Frequency [Hz] Modal damping ratio [%]

1st Translational mode 4.80 4.3

1st Torsional mode 9.23 2.5

4.42 Hz 9.09 Hz 13.30 Hz 14.97 Hz(a)

9.85 Hz 14.46 Hz 17.31 Hz 20.05 Hz(b)

FIGURE 10 Calculated mode shapes in the: (a) transversal direction; (b) longitudinal

direction.



consuming and the response spectrum of Type 1 (interplate earthquake) is usually more

stringent for Lisbon area and for the type of structures being considered, only one type of

earthquake was considered.

It is noted that a response spectrum is a spectral representation of the peak response of

single degree of freedom system with a given common damping z and natural periods

Tn (varying from aminimum value up to amaximum value) to a given seismic inputmotion.

Thus, for a given input motion, it is possible to obtain several response spectra associated

with different values of damping adopted. The process of generating time histories compa-

tible with the input for a response spectrum is therefore independent of the damping

considered. Concerning the codes, Eurocode 8 clearly defines that the artificial accelero-

grams shall be generated so as tomatch the elastic response spectra for 5%viscous damping.

Using the 1:3 reduced scale, the accelerograms have a total duration of 6 s, from

which 3.33 s correspond to the intense phase, and a PGA equal to 4.51 m/s2.

4.2. Analysis Tools

Nonlinear time history analysis onmasonry structures is complex and takes a long time for the

model considered. In opposition to the typical framed concrete structures, where it is easy to

identify the yield hinges, masonry buildings have distributed cracking around the structure,

which features opening, closing and reopening, due to the low value of the tensile strength.

The quasi-brittle masonry behavior in tension introduces numerical noise, due to the fast

transition from linear elastic behavior to a fully cracked state involving an almost zero

stiffness. The quasi-instantaneous changes in the displacement field tend to originate the

propagation of high frequency spurious vibrations [Cervera et al., 1995]. Therefore, it is

important to adopt the Hilber-Hughes-Taylor time integration method [DIANA, 2005] (also

called the amethod), whichwas used herewith a equal to –0.1.With thismethod it is possible

to introduce numerical dissipation without degrading the accuracy. The Hilber-Hughes-

Taylor method uses the same finite difference equations as the Newmark method with:

� ¼ 1

2ð1� 2�Þ (7)

and

� ¼ 1

4ð1� �Þ2: (8)

For a = 0 the method reduces to the Newmark method. For �1/3 = a = 1/2 the

scheme is second-order accurate and unconditionally stable. Decreasing a means increas-

ing the numerical damping, and the adopted damping is low for low-frequency modes and

high for the high-frequencies modes.

The time stepDtwas determined using Eq. (9), in order to account for the lowest period

with relevance in the structural behavior Ti, with an error lower than 5%. It was assumed that

Tiwas equal to 0.025 s [Mendes and Lourenco, 2008], meaning thatDt is equal to 0.00125 s.

�t ¼ 1

20Ti (9)

Concerning the iteration method, the regular Newton-Raphson method, in which

the tangential stiffness is set up before each iteration, was used. In the equilibrium



iteration process, a convergence criterion based on the internal energy and a tolerance

equal to 10�3 was used.

4.3. Results

In the numerical modeling the time series were applied directly with the prescribed code

value. It is noted that in the experimental testing the time series were imposed with

increasing amplitude and this can influence the final results, although the final crack

pattern did not change significantly.

Figure 11 presents the maximum values of the tensile principal strains e1 for the threeearthquake records. The results indicate that the facades at the 4th floor and the base of the

structure are the zones of larger damage concentration, being the high level of damage in

the 4th floor’s piers highlighted.

The relation between the ‘‘seismic coefficient’’ ah defined by Eq. (10) and the

horizontal displacement at the top of the structure was plotted. The envelopes of these

relations, for the different earthquakes and directions, are presented in Figs. 12 and 13.

It is observed that the maximum values of ah are about 0.2 and 0.65 in the transversal

and longitudinal directions, respectively (approximately a relation 100% longitudinal

‘‘+‘‘ 31% transversal).

�h ¼P

Horizontal forces

Self weight of the structure(10)

5. Nonlinear Static (Pushover) Analyses

5.1. Capacity Curves

In the pushover analysis the capacity curves was considered by increasing a set of lateral

loads applied to the structure in two independent directions. Two vertical distributions of

lateral loads were used: (a) uniform pattern, based on lateral forces proportional to mass

regardless of elevation – uniform response acceleration; (b) modal pattern, proportional to

forces consistent with the 1st mode shape in the applied direction. In an attempt to explore

the pushover analyses proportional to the 1st mode shape, an additional adaptive pushover

analysis was also carried out.

In the pushover analysis physical and geometrical nonlinear behavior was consid-

ered, even if it is expected that the geometrical nonlinear effects have minor influence in

the maximum load.

FIGURE 11 Tensile principal stains (outside surface): (a) earthquake 1; (b) earthquake 2;

(c) earthquake 3.



For the solution procedure, the regular Newton-Raphson method, the line search

algorithm and the arc-length control were used.

5.2. Pushover Analysis Proportional to the Mass

The capacity curves of the pushover analyses proportional to the mass show that

the maximum seismic coefficients are higher than the dynamic analysis (about 24%)

(Fig. 14).

–0.8

–0.6

–0.4

–0.2

0

0.2

0.4

0.6

0.8

–0.01 –0.0075 –0.005 –0.0025 0 0.0025 0.005 0.0075 0.01

Displacement[m]

Seis

mic

coe

ffic

ient

[α

h]

Earthquake 1Earthquake 2Earthquake 3

Earthquake 1

FIGURE 13 Envelope of the relation between the horizontal displacement (4th floor) and

the seismic coefficient in the longitudinal direction.

–0.4

–0.3

–0.2

–0.1

0

0.1

0.2

0.3

0.4

–0.04 –0.03 –0.02 –0.01 0.00 0.01 0.02 0.03 0.04

Displacement[m]

Seis

mic

coe

ffic

ient

[α

h]


Earthquake 1

FIGURE 12 Envelope of the relation between the horizontal displacement (4th floor) and

the seismic coefficient in the transversal direction.



In the pushover analysis proportional to the mass, the damage concentration only

appears at the lower zone of the structure (Fig. 14). It is noted that in the dynamic analysis

the damage concentrates at the 4th floor (facades) and at the base (Fig. 11). Thus, this

pushover analysis does not simulate correctly the performance of ‘‘gaioleiro’’ buildings

under seismic load.

5.3. Pushover Analysis Proportional to the 1st Mode Shape

The capacity curves of the pushover analysis proportional to the 1st mode (in the applied

direction) show that the maximum seismic coefficients approach the dynamic analysis.

The crack patterns only provide in plane damage, which is not in agreement with the

out-of-plane mechanism found in the time integration analysis and shaking table test

(Fig. 15). Hence, the damage at the upper stories must have a significant contribution

from the higher modes, including the local modes of the piers.

5.4. Adaptive Pushover Analysis

In the adaptive pushover analysis the lateral loads, proportional to the 1st mode shape in

the applied direction were updated as a function of the existing damage. Here, the aim is

to understand how the update of the external load vector can influence the structure

response.

The analysis was done in four phases and after each phase the new modal shape was

calculated by using the tangential stiffness matrix (Eq. (11)), allowing the updating of the

load distribution as function of the damage,

0

0.05

0.1

0.15

0.2

0.25

0.3

0 0.01 0.02 0.03 0.04 0.05

Displacement [m]

Seis

mic

coe

ffic

ient

[α h

] Se

ism

ic c

oeff

icie

nt [

α h]

PushoverDynamic

Point 1

(a)

Point 2

0

0.2

0.4

0.6

0.8

1

0 0.005 0.01 0.015 0.02

Displacement [m]

PushoverDynamic

Point 3

(b)

Point 4

P1

P2

1 [m/m] 1 [m/m]

1 [m/m] 1 [m/m]

P3

P4

FIGURE 14 Capacity curves and tensile principal strains of the pushover analysis

proportional to the mass in the: (a) transversal direction; (b) longitudinal direction.



kt � w2i M

� ��i ¼ 0; (11)

where

kt is the tangential stiffness matrix;

wi is the angular frequency;

M is the mass matrix;

�i is the mode shape vector:

The adaptive pushover analysis (Fig. 16a) in the transversal direction presents a

decrease of the maximum seismic coefficient (about 21% of the maximum seismic

coefficient of the pushover analysis proportional to the 1st mode in the corresponding

direction). Since the lintels crack progressively, the update of the load distribution has

influence in the structure behavior. The crack pattern (Fig. 17a) presents damage con-

centration in the lintels and at the base.

In the longitudinal direction the adaptive pushover analysis (Figs. 16b and 17b)

provides the same behavior of the pushover analysis proportional to the 1st mode in the

corresponding direction. In fact, in the longitudinal direction the structure is very stiff,

when compared to the transversal direction. Up to the maximum seismic coefficient the

damage is almost non-existent and after reaching this value, the structure presents a brittle

behavior. So, in this direction the update of the load distribution does not have influence

in the response.

Deslocamento [m]

0

0.05

0.1

0.15

0.2

0.25

0.3

0 0.01 0.02 0.03 0.04 0.05

Displacement [m]

PushoverDynamic

Point 1

(a)

Point 2

0

0.2

0.4

0.6

0.8

1

0 0.005 0.01 0.015 0.02

Displacement [m]

PushoverDynamic

Point 3

(b)

Point 4

P1

P2

1 1

1 1 P3

P4

Seis

mic

coe

ffic

ient

[α

h]

Seis

mic

coe

ffic

ient

[α

h]

FIGURE 15 Capacity curves and tensile principal strains of the pushover analysis

proportional to the 1st mode shape in the: (a) transversal direction; (b) longitudinal

direction.



6. Discussion About the Collapse Mechanisms Found

The ‘‘gaioleiro’’ buildings under seismic load present a damage concentration at the 4th

floor (facades) and at the base (Fig. 11), being this result a combination of in-plane and

out-of-plane actions. The damage represents the typical failure mechanism of masonry

buildings (Fig. 18): (a) cracking around the corners of the openings; (b) out-of-plane

collapse (4th floor’s piers). The different pushover analyses performed in this work could

not simulate correctly the damage of the structure.

The analysis of the collapse mechanism in terms of displacements at floor levels

(or drifts) does not characterize the observed crack patterns. In case of the time integra-

tion analysis, the maximum out-of-plane displacement is equal to 10 mm and a correla-

tion between the out-of-plane drift and damage would indicate a maximum damage

between the ground and the first floor level (Fig. 19). Thus, in opposition to framed

concrete structures, the evaluation of results at the floor levels is not enough to identify

correctly the zones of largest damage of masonry buildings.

FIGURE 17 Tensile principal strains (outside surface) of the adaptive pushover analysis

in the: (a) transversal direction; (b) longitudinal direction.

0

0.05

0.1

0.15

0.2

0.25

0.3

0 0.01 0.02 0.03 0.04 0.05Displacement [m]

Seis

mic

coe

ffic

ient

[α h

]

Seis

mic

coe

ffic

ient

[α h

]

PushoverDynamic

0

0.2

0.4

0.6

0.8

1

0 0.005 0.01 0.015 0.02Displacement [m]

PushoverDynamic

(a) (b)

FIGURE 16 Capacity curves of the adaptive pushover analysis in the: (a) transversal

direction; (b) longitudinal direction (the points delimit the phases).



As a complement to the interstory results, vertical alignments were defined. In these

alignments the maximum displacements and the maximum slopes, in terms of in-plane

and out-of-plane displacement, were plotted. Here, the slope is equal to the relative

displacement between the node and the lower floor, divided by the relative vertical

direction (Eq. (12) and Fig. 20). It is noted that when the first and the last nodes of the

floor are used, the slope is equal to the typical interstory drift.

Slope Nj ni ¼ uni � uNj

hni � hNj

�� (12)

Figure 21 shows the maximum out-of-plane displacement of a quarter of the struc-

ture. Through this representation it is observed that in the facades the displacements

increase from the border to the center of the wall and the maximum out-of-plane

displacement take place at the 4th floor’s pier (about 16 mm) and not at the top of the

structure (10 mm). In the side gable walls the maximum out-of-plane displacement takes

place at the top of the structure (about 32 mm) both at the border and central alignment.

FIGURE 18 Details of the earthquake 1 damage (wk is the crack width obtained by

integrating the strains).

0

1.2

2.4

3.6

4.8

0 2 4 6 8 10 12

Hei

ght

[m]


3

0

1.2

2.4

3.6

4.8

0 0.1 0.2 0.3 0.4 0.5Maximum drift [%]

Hei

ght

[m]


3

(a) (b)

Maximum displacement [m]

FIGURE 19 Results at the central alignment of the facade: (a) maximum out-of-plane

displacement; (b) maximum drift.



The plot of the maximum out-of-plane slope (Fig. 22) indicates that the central 4th

floor’s piers and the base of the structure are the zones of largest damage (slopes higher

than 1%), in agreement with the crack patterns of the dynamic analysis.

The in-plane results indicate that the maximum displacement of the facades is equal

to 32 mm (top of the structure), without meaningful differences between the central and

the border alignments. In the side-walls the maximum displacement is about 11 mm (top

of the structure) and no meaningful differences were found between the central and

Nj is the node at the j floor level (j = 1,2,…4) or at the base level (j = 0)

ni is the node i among floors (i = 1,…,m)

u is the out-of-plane relative displacement

u = unj+4 – uNj

h is the relative height h = hnj+4 – hNj

u

h

Nj

ni+4

Slope [Nj ni+4]

Nj

ni

ni+1

nm

Nj+1

Masonry wall

Finite element mesh

FIGURE 20 Definition of out-of-plane slope.

0

1.2

2.4

3.6

4.8

0 5 10 15 20Maximum displacement [m]

Hei

ght

[m]


(*1E-3)

1

0

1.2

2.4

3.6

4.8

0 5 10 15 20

Maximum displacement [m]

Hei

ght

[m]

(*1E-3)

3


0

1.2

2.4

3.6

4.8

0 5 10 15 20 25 30 35Maximum displacement [m]

Hei

ght

[m]

(*1E-3)

12Earthquake 1Earthquake 2Earthquake 3

0

1.2

2.4

3.6

4.8

0 5 10 15 20 25 30 35Maximum displacement [m]

Hei

ght

[m]

(*1E-3)


FIGURE 21 Maximum out-of-plane displacement.



the border alignments. However, the sharp increase of the displacement at the base is

highlighted on the plots (Fig. 23).

Concerning the maximum in-plane slope (Fig. 24), it is verified that in the facades

the maximum values occur at the base of the structure (larger than 2%) and in the 2nd to

0

1.2

2.4

3.6

4.8

0 0.25 0.5 0.75 1 1.25 1.5Maximum slope [%]

Hei

ght [

m]


0

1.2

2.4

3.6

4.8

0 0.25 0.5 0.75 1 1.25 1.5Maximum slope [%]

Hei

ght [

m]


3

0

1.2

2.4

3.6

4.8

0 0.5 1 1.5 2 2.5 3

Maximum slope [%]

Hei

ght [

m]


12

0

1.2

2.4

3.6

4.8

0 0.5 1 1.5 2 2.5 3Maximum slope [%]

Hei

ght [

m]


13

FIGURE 22 Maximum out-of-plane slope.

0

1.2

2.4

3.6

4.8


Hei

ght [

m]

(*1E-3)

1


0

1.2

2.4

3.6

4.8


Hei

ght

[m]

(*1E-3)

3


0

1.2

2.4

3.6

4.8

0 2 4 6 8 10 12Maximum displacement [m]

Hei

ght

[m]

(*1E-3)

12


0

1.2

2.4

3.6

4.8

0 2 4 6 8 10 12Maximum displacement [m]

Hei

ght

[m]

(*1E-3)

13


FIGURE 23 Maximum in-plane displacement.



4th floors the maximum slope is about 0.75%. In the side-walls the maximum slope takes

place also at the base of the structure (larger than 1.5%). However, in the 2nd–4th floors of

the side-walls the in-plane slope is only about 0.2% (walls without openings).

Through the combined effects of in-plane and out-of-plane results, it is concluded

that the side-walls present a damage concentration at the base of the structure. But

the facades are the most vulnerable walls, being possible to identify damage at the

base, cracking around the corners of the opening corners and out-of-plane collapse of

the 4th floor’s piers. Thus, the use of the displacements and the slopes, using the nodes of

the finite element mesh, is in agreement with the crack patterns, representing good

indicators of damage.

7. Conclusions

Through a nonlinear time history analysis it was observed that the buildings of

‘‘gaioleiro’’ type with appropriate floor-wall connection, under seismic action (Lisbon

zone and soil of the type A) are in the limit of their loading capacity according to the

earthquake action proposed in the new Eurocode 8 National Annex. Therefore, it seems

that a strong floor-wall connection is not enough to guarantee the good performance of

the building under seismic load, due to the floors flexibility.

The ‘‘gaioleiro’’ buildings present the typical collapse of masonry buildings includ-

ing: (a) cracking around the corners of the openings; (b) out-of-plane collapse (4th floor’s

piers). The displacements at floor levels and the interstorey drifts are not appropriate to

detect the damaged zones of the structure, as the maximum amplitudes of the response

do not occur at floor levels. The plot of displacements and slope, using the nodes of the

finite elements mesh into vertical alignments seem good indicators of damage. Thus,

0

1.2

2.4

3.6

4.8

0 0.5 1 1.5 2 2.5

Maximum slope [%]

Hei

ght [

m]


1

0

1.2

2.4

3.6

4.8

0 0.5 1 1.5 2 2.5Maximum slope [%]

Hei

ght

[m]


3

0

1.2

2.4

3.6

4.8

0 0.5 1 1.5 2 2.5Maximum slope [%]

Hei

ght [

m]


12

0

1.2

2.4

3.6

4.8

0 0.5 1 1.5 2 2.5Maximum slope [%]

Hei

ght [

m]


13

FIGURE 24 Maximum in-plane slope.



the evaluation of the structural behavior of masonry buildings should take into account

points in between floors, namely in the upper floors.

With respect to pushover analyses (proportional to the mass or to the 1st mode), it

was concluded that these do not simulate correctly the failure mode of the structure,

meaning that vibration modes with higher frequencies have a significant contribution to

the behavior. The pushover analysis proportional to the 1st mode shape performed better

in terms of load-displacement diagram than the pushover analysis proportional to the

mass, simulating correctly the in-plane behavior.

In an attempt to explore the nonlinear static analyses proportional to the 1st mode

shape, an adaptive pushover analysis was carried out, in which the load distribution was

updated as a function of the existing damage. This analysis did not provide any improve-

ment in terms of load-displacement diagrams or failure mechanisms.

The news versions of nonlinear static analyses (for instance the Modal Pushover

Analysis introduced by Chopra and Goel (2002) or the Adaptive Capacity Spectrum

Method recently proposed by Casarotti and Pinho (2007)) include the effects of

higher modes of vibration and should be tested for the ‘‘Gaioleiro’’ buildings in

some future work.

Even if the structure analyzed presents regularity in plan and in elevation, the

flexible floors are most likely the reason for the deficient performance of the pushover

analysis.

Acknowledgments

The authors are grateful to the National Laboratory of Civil Engineering for providing the

experimental data for the shaking table tests. The present work is partly funded by FCT

(Portuguese Foundation for Science and Technology), through project POCI/ECM/61671/

2004, ‘‘Seismic vulnerability reduction of old masonry buildings’’ and PhD grant SFRH/

BD/32190/2006.

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LESSLOSS final workshop, Sub-project 7 - Vulnerability reduction in structures.



seismic assessment of masonry ‘‘gaioleiro’’...

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